An interval solution for the n-th order linear ODEs with interval initial conditions

In this paper, a new method for interval solution of the order linear ordinary differential equations (ODEs) with interval initial conditions is constructed. In this approach, by using the Neher\u27s algorithm cite{ref1}, first we obtain a guaranteed enclosure solution for an initial point value problem and then based on the Moore\u27s idea cite{ref2021,ref3}, we transform this solution to arrive at an interval solution for the main problem. For the sake of clarity, we present an algorithm in terms of the linear second order ODEs ($n=2$). Finally, some numerical examples are presented to demonstrate the efficiency of the proposed algorithm